Applications of Image Filters

Transcription

1 02/04/0 Applications of Image Filters Computer Vision CS 543 / ECE 549 University of Illinois Derek Hoiem

2 Review: Image filtering g[, ] f [.,.] h[.,.] h[ m, n] = k, l f [ k, l] g[ m + k, n + l] Credit: S. Seitz

3 Image filtering g[, ] f [.,.] h[.,.] h[ m, n] = k, l f [ k, l] g[ m + k, n + l] Credit: S. Seitz

4 Image filtering g[, ] f [.,.] h[.,.] h[ m, n] = k, l f [ k, l] g[ m + k, n + l] Credit: S. Seitz

5 Filtering in spatial domain * =

6 Filtering in frequency domain FFT FFT Inverse FFT

7 Sharpening revisited What does blurring take away? = original smoothed (5x5) detail Let s add it back: + α = original detail sharpened

8 Application: Hybrid Images A. Oliva, A. Torralba, P.G. Schyns, Hybrid Images, SIGGRAPH 2006

9 Application: Hybrid Images A. Oliva, A. Torralba, P.G. Schyns, Hybrid Images, SIGGRAPH 2006

10 Today s class How to use filters for Matching Denoising Anti aliasing Image representation with pyramids Texture What is it? How to represent it?

11 Matching with filters Goal: find in image

12 Matching with filters Goal: find in image Method : SSD Input - sqrt(ssd) Threshold at 0.8

13 Matching with filters Goal: find in image Method : SSD Method 2: Normalized cross correlation Input Normalized X-Correlation Threshold at 0.5

14 Noise + = Gaussian Additive Noise Noisy Image

15 Gaussian noise Mathematical model: sum of many independent factors Assumption: independent, zero mean noise Source: M. Hebert

16 Noise Original Salt and pepper noise Salt and pepper noise: contains random occurrences of black and white pixels Impulse noise: contains random occurrences of white pixels Gaussian noise: variations in intensity drawn from a Gaussian normal distribution Impulse noise Gaussian noise Source: S. Seitz

17 Denoising Gaussian Filter Additive Gaussian Noise

18 Reducing Gaussian noise Smoothing with larger standard deviations suppresses noise, but also blurs the image Source: S. Lazebnik

19 Reducing salt and pepper noise by Gaussian smoothing 3x3 5x5 7x7

20 Alternative idea: Median filtering A median filter operates over a window by selecting the median intensity in the window Is median filtering linear? Source: K. Grauman

21 Median filter What advantage does median filtering have over Gaussian filtering? Robustness to outliers Source: K. Grauman

22 Median filter Salt-and-pepper noise Median filtered MATLAB: medfilt2(image, [h w]) Source: M. Hebert

23 Median vs. Gaussian filtering 3x3 5x5 7x7 Gaussian Median

24 Subsampling by a factor of 2 Throw away every other row and column to create a /2 size image

25 Aliasing problem D example (sinewave): Source: S. Marschner

26 Aliasing problem D example (sinewave): Source: S. Marschner

27 Aliasing problem Sub sampling may be dangerous. Characteristic errors may appear: Wagon wheels rolling the wrong way in movies Checkerboards disintegrate in ray tracing Striped shirts look funny on color television Source: D. Forsyth

28 Aliasing in video Slide by Steve Seitz

29 Aliasing in graphics Source: A. Efros

30 Sampling and aliasing

31 Nyquist Shannon Sampling Theorem When sampling a signal at discrete intervals, the sampling frequency must be 2 f max ; f max = max frequency of the input signal. This will allows to reconstruct the original perfectly from the sampled version v v v good bad

32 Anti aliasing Solutions: Sample more often Get rid of all frequencies that are greater than half the new sampling frequency Will lose information But it s better than aliasing Apply a smoothing filter

33 Algorithm for downsampling by factor of 2. Start with image(h, w) 2. Apply low pass filter im_blur = imfilter(image, fspecial( gaussian, 7, )) 3. Sample every other pixel im_small = im_blur(:2:end, :2:end);

34 Anti aliasing Forsyth and Ponce 2002

35 Subsampling without pre filtering /2 /4 (2x zoom) /8 (4x zoom) Slide by Steve Seitz

36 Subsampling with Gaussian pre filtering Gaussian /2 G /4 G /8 Slide by Steve Seitz

37 Gaussian pyramid Source: Forsyth

38 Laplacian filter unit impulse Gaussian Laplacian of Gaussian Source: Lazebnik

39 Laplacian pyramid Source: Forsyth

40 Computing Gaussian/Laplacian Pyramid Can we reconstruct the original from the laplacian pyramid?

41 Related idea: 2d wavelets

42 2d Wavelets Matlab: wavemenu

43 Image representation Pixels: great for spatial resolution, poor access to frequency Fourier transform: great for frequency, not for spatial info Pyramids/wavelets: balance between spatial and frequency information

44 Major uses of image pyramids Compression Object detection Scale search Features Detecting stable interest points Registration Course to fine

45 Texture Source: Forsyth

46 Texture and Material

47 Texture and Orientation

48 Texture and Scale

49 What is texture? Regular or stochastic patterns caused by bumps, grooves, and/or markings

50 How can we represent texture? Measure frequencies at various orientations and scales

51 Overcomplete representation: filter banks LM Filter Bank Code for filter banks:

52 Filter banks Process image with each filter and keep responses (or squared/abs responses)

53 Representing texture Idea : take simple statistics (e.g., mean, std) of various absolute filter responses

54 Can you match the texture to the response? Filters A B 2 C 3 Mean abs responses

55 Representing texture by mean abs response Filters Mean abs responses

56 Representing texture Idea 2: take vectors of filter responses at each pixel and cluster them, then take histograms (more on in coming weeks)

57 Things to remember When matching using a filter, normalized cross correlation is preferred Use Gaussian or median filter for denoising Beware of aliasing use lowpass filter to downsample Laplacian pyramids and wavelets provide spatial/frequency information Filter banks provide overcomplete representation, good for modeling/recognizing texture

58 Next class Edges and lines

59 Questions